It is unbelievable that the review is made in 2013. Many decades passed after oriental scholars and some others established that the so-called Aryan migration to India is a myth. Max Muller himself admitted that if at all a race called Aryan existed, withdrawing his own earlier statements! However, I admire his interest in this book.
Anyway, any book of this nature, that too having its birth in such a period as its, coming from a total outsider is commendable.

I would give it 10 stars if I could. Countless Vedic Students and Scholars have been inspired and motivated by this book. I would recommend an intermediate level Classic/Epic Sanskrit before attempting this.
30 of the 1,028 hymns of the Rig Veda are examined in detail. It appears that the Samhita, Pada texts and commentary excerpts of Sayana used here should be attributed to Max Mullers Rig Veda Edition (compiled over a period of 25 years).
Insightful introduction, note section: 4 "Arrangement of the Rig Veda". These hymns were originally passed on for hundreds of years, by Aryan tribes migrating into India strictly by memory (pitched accents, metre, mnomics etc. as memory devices). Hymns were compiled at the Kuru capital Kurushektra.
Book is keyed to correspond with the Authors Vedic Grammar. However, this is not always seamless! Searching Grammar topics online is a possible option.
Currently, there is confusion regarding print Editions of the book that are complete! I'm a traditionalist; however, Digital versions may be the preferred choice.
In addition to this extraordinary nature oriented verse, actual history is recorded indicating the Aryan migration path and possibly climate change in the form of Drought: Indra/Vrtra myth and the releasing of the "waters". Furthermore, Mandukas (Frogs) pg 141-147.
One historical note I believe needs to be adressed, the use of the term dasa or dasyo to designate "dark aborigines". The original inhabitants of India were tribes from Africa, long before the arrival of the Aryans. The "Dasa" of the Rig Veda or "Daha" of the Iranian Avesta may have been the earliest Aryans to arrive in India who were engaged in conflict with the subsequently arriving Rig Vedic Aryans and were pushed to the perimeter and not originally the Indigenous Black Tribes of India.
Each selection has an insightful introduction which is a condensed version of the Authors: "Vedic Mythology".
Initial reaction of the English translations offer up here maybe somewhat lukewarm. However, with increased knowledge of the Language, beliefs, history, etc. you may agree with me...what a Extraordinary Legacy this is.